Mathematical Optimization of Drug Regimens Improvements in drug regimens can make a difference in both clinical trial success and patient outcomes. Optimal control can be used to mathematically optimize regimens, which can then be tested experimentally and clinically. I will show examples of optimization of regimens for math models of various diseases, and discuss some …
Simplifying Soil Organic Carbon Model Structures with First-Order Linear Decay: When, How, and Why? Soil organic matter is the largest terrestrial pool of carbon on Earth, containing more carbon than terrestrial vegetation and more carbon than even the atmosphere. Most Earth System Models (ESMs), designed to integrate and examine how the interdependent systems of the …
Turing Patterns as a Model for Brain Folding Development Neuroscientists are interested in correlating brain function with anatomy. However, the highly complex folding patterns of the brain and the high variability in folding patterns across individuals contribute to the difficulty in understanding healthy brain function and disease. Interestingly, there is no consensus in neurobiology as …
The Eye-Lens Growth Model Biological lens in the eye of a mammal focuses light on the retina. Its shape and size is crucial for that purpose. We provide the first ever mathematical growth model of the mouse eye-lens and succeed in capturing a variety of behavior about the size of the lens, number of cells …
Chaos and homeostasis in multiple timescales dynamics Complex nonlinear and network dynamics, as observed in many biological systems, are prone to generate complex chaotic activity. Fortunately, in nature, these systems are still able to maintain essential biological function, and may be robust to changes in the environment despite their chaotic nature, until they break down …
Cytoneme-mediated morphogenesis Morphogen protein gradients play an essential role in the spatial regulation of patterning during embryonic development. The most commonly accepted mechanism of protein gradient formation involves the diffusion and degradation of morphogens from a localized source. Recently, an alternative mechanism has been proposed, which is based on cell-to-cell transport via thin, actin-rich cellular …
Unraveling Lassa Fever Persistence: A Compartmental Model with Environmental Virus-Host-Vector Interaction Lassa fever (LF), a severe viral hemorrhagic disease transmitted by rodents, particularly Mastomys natalensis, is endemic in West Africa, notably Nigeria, with substantial morbidity and mortality rates. Existing mathematical models on LF lack integration of the crucial environmental component, overlooking transmission through contaminated surfaces. Moreover, …
Sensitivity, Bifurcation, and Stochastic Analysis of Tuberculosis Progression Mycobacterium tuberculosis infection features various disease outcomes: clearance, latency, active disease, and latent tuberculosis infection (LTBI) reactivation. Identifying the decisive factors for disease outcomes and progression is crucial to elucidate the macrophages-tuberculosis interaction and provide insights into therapeutic strategies. To achieve this goal, we first model the …
Optimal control of combination immunotherapy in a glioblastoma-immune dynamics model Glioblastoma (GBM) is the most common type of primary brain tumor. It is very aggressive with minimally effective treatment options. Current therapies yield a median survival of 15 months. Treatment failure may be caused by the highly immune-suppressed glioma microenvironment, leading to a rise in …
Data Assimilation in Medical Models and Digital Twins One of the growing areas of interest in the context of biological and medical models is the question of how to personalize a model to a target organism or patient in order to improve model predictions. This question is inherently tied to data assimilation (DA): the process …
